Question

Solve for $x$:

${\log }_{e}2.{\log }_{x}625={\log }_{10}16.{\log }_{e}10$

Answer 1

Given,

$lo{g}_e^2\cdot lo{g}_x^{625}=lo{g}_{10}^{16}\cdot lo{g}_e^{10}$

or, $lo{g}_e^{2}lo{g}_x^{5^4}=lo{g}_e^{16}$

or, $lo{g}_e^2\cdot lo{g}_x^{5^4}=4lo{g}_e^2$

or, $5^9=x^5$

or, $x=5$.